Thanks to everyone who replied, on and off list.  It seems that
better fillers are available than I was aware.  The holes don't ever
need to hold a screw again (they really are a mystery) and are deep
inside the works, and I doubt I will match the tone of the original
wood anyway (some is stained - why did they stain parts you can't
see?) so I fear a hacky appearance is inevitable -- but nevertheless
I'll give plug cutters a go first.

Funnily enough, they're one of the few things I've not tried.  In
non-musical woodwork where damage is visible I've generally used
a chisel to cut rectangular holes to insert pieces of replacement wood
and plane down, which can look fine on the surface, but I don't trust
myself to do that in a way that's wholly airtight.  That was my worry
with the dowel method as well, which I've used before and done fine,
but not generally been impressed with.

Plug cutters sound like a better bet and maybe easier than I feared;
I've ordered some that claim to have a slight taper in the hope of
a super-tight fit and corresponding lack of leakage.

Thanks again,

Lester Hawksby